This paper is on the asymptotic behavior of elastic string equation with localized degenerate Kelvin–Voigt damping u t ( x , ) − [ + b ] = 0 ∈ 1 > \begin{equation} u_{tt}(x,t)-[u_{x}(x,t)+b(x) u_{xt}(x,t) ]_{x}=0,\; x\in (-1,1),\; t>0, \end{equation} (0.1)where $b(x)=0$ $x\in (-1,0]$ and α $b(x)=x^\alpha >0$ (0,1)$ for $\alpha \in . It known that optimal decay rate solution 2 $t^{-2}$ in limit ...

The renormalization group approach towards the string representation of non abelian gauge theories translates, in terms of the string sigma model beta function equations, the renormalization group evolution of the gauge coupling constant and Zamolodchikov‘s c function. Tachyon stability, glueball mass gap, renormalization group evolution of the c function and the area law for the Wilson loop ar...

The functional transformationmethod (FTM) is a well-establishedmathematical method for accurate simulations of multidimensional physical systems from various fields of science, including optics, heat andmass transfer, electrical engineering, and acoustics. This paper applies the FTM to real-time simulations of transversal vibrating strings. First, a physical model of a transversal vibrating los...

The theta dependence of the vacuum energy in large N Yang-Mills theory has been studied some time ago by Witten using a duality of large N gauge theories with string theory compactified on a certain space-time. We show that within the field theory context vacuum fluctuations of the topological charge give rise the vacuum energy consistent with the string theory computation. Furthermore, we calc...